On the rare occasions I get a text, it warns me of the delay but makes no mention of changing my check in time. Of course one makes assumptions, but the normal advice is to check in as per MMB unless told very specifically differently, and that text message is no such thing.

However I must admit in these situations I do track the inbound flight and make a judgement call. I like to get 2 sources of information, so I also check on something like flightaware.com. However I'm always hand luggage only and always printing my own boarding pass, which is very relevant since at some locations they simply won't take checked luggage in late, even if the plane is late (e.g. if baggage handlers are on fixed shifts).

But that's a risk I take. The cardinal rule is always check in according to the original time unless very clearly told differently. It also says that with ba.com too.